LZ77 compression

The first algorithm to use the Lempel-Zivsubstitutional
compression schemes, proposed in 1977. LZ77 compression
keeps track of the last n bytes of data seen, and when a
phrase is encountered that has already been seen, it outputs a
pair of values corresponding to the position of the phrase in
the previously-seen buffer of data, and the length of the
phrase. In effect the compressor moves a fixed-size "window"
over the data (generally referred to as a "sliding window"),
with the position part of the (position, length) pair
referring to the position of the phrase within the window.

The most commonly used algorithms are derived from the
LZSS scheme described by James Storer and Thomas Szymanski
in 1982. In this the compressor maintains a window of size N
bytes and a "lookahead buffer", the contents of which it tries
to find a match for in the window:

while (lookAheadBuffer not empty)
{
get a pointer (position, match) to the longest match in
the window for the lookahead buffer;
if (length > MINIMUM_MATCH_LENGTH)
{
output a (position, length) pair;
shift the window length characters along;
}
else
{
output the first character in the lookahead buffer;
shift the window 1 character along;
}
}

Decompression is simple and fast: whenever a (POSITION,
LENGTH) pair is encountered, go to that POSITION in the window
and copy LENGTH bytes to the output.

Sliding-window-based schemes can be simplified by numbering
the input text characters mod N, in effect creating a circular
buffer. The sliding window approach automatically creates the
LRU effect which must be done explicitly in LZ78 schemes.
Variants of this method apply additional compression to the
output of the LZSS compressor, which include a simple
variable-length code (LZB), dynamic Huffman coding
(LZH), and Shannon-Fano coding (ZIP 1.x), all of which
result in a certain degree of improvement over the basic
scheme, especially when the data are rather random and the
LZSS compressor has little effect. An algorithm was developed
which combines the ideas behind LZ77 and LZ78 to produce a
hybrid called LZFG. LZFG uses the standard sliding window,
but stores the data in a modified trie data structure and
produces as output the position of the text in the trie.
Since LZFG only inserts complete *phrases* into the
dictionary, it should run faster than other LZ77-based
compressors.

LZ78 compression

A substitutional compression scheme which works by entering
phrases into a dictionary and then, when a reoccurrence of
that particular phrase is found, outputting the dictionary
index instead of the phrase. Several algorithms are based
on this principle, differing mainly in the manner in which
they manage the dictionary.

The most well-known Lempel-Ziv scheme is Terry Welch's
Lempel-Ziv Welch variant of LZ78.